Without kinetic and potential energy cross country skiing would be extremely
boring. There would not be the frustration of trying to maneuver up
hill, only to slide down backwards in a failed attempt. Skiers would
also miss out on screaming down those hills and crashing into a snow bank.

Lets assume that energy is conserved when a cross country skier decides
to conquer a mountain. When the skier is at the bottom of the hill their
kinetic energy is at it's maximum and their potential energy is at zero.
As the skier maneuvers up the hill their kinetic energy slowly decreases
at the same rate that their potential energy increases. When the skier
is halfway up the hill the kinetic and potential energies are equal. A
few hours later when the skier has reached the top of the mountain, their
potential energy is at its maximum and their kinetic energy is zero.

Kinetic energy is one half times the mass times the velocity squared.
Kinetic energy = 1/2mv2. Potential
energy is the mass times gravity times the height. Potential Energy
= m*g*h. Conservation of energy states that Ki+ Pi = Kf
+ Pf. This simply means that the sum of the
skiers initial potential and kinetic energy is equal to the sum of the skiers
final potential and kinetic energy.

With the potential energy at its maximum the skier decides to risk
it all and descend. Mirroring the effects of climbing the hill, the
skier slowly loses potential energy the farther down the hill the skier
is. This causes the skier's kinetic energy to increase, as predicted
by conservation of energy. When the skier is at the bottom of the hill,
the potential energy has dropped to zero and kinetic energy is once again
at its maximum.

Depending on the friction of the snow on the skier, the skier would slow
down and come to a rest sometime after reaching the bottom of the hill.
The animation below illustrates this concept very well. As the
skier goes down the hill, the Kinetic Energy, Potential Energy, Work, and
Total Mechanical Energy bars reflect what is happening in the system.

There are some flaws in the ideal scenario above.
Cross-country skiers are constantly effected by friction which is not
a conservative force. Air resistance and the use of poles are also
factors which effect conservation of energy. Despite these outside
influences, the animation above still gives a general idea of what happens
to work and energy when a skier goes down hill.